Question: Simplify the following expression: $q = \dfrac{1}{2y} - \dfrac{1}{6y}$
Solution: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $2y$ and $6y$ $\lcm(2y, 6y) = 6y$ $ q = \dfrac{3}{3} \cdot \dfrac{1}{2y} - \dfrac{1}{1} \cdot \dfrac{1}{6y} $ $q = \dfrac{3}{6y} - \dfrac{1}{6y}$ $q = \dfrac{3 -1}{6y}$ $q = \dfrac{2}{6y}$ Simplify the expression by dividing the numerator and denominator by 2: $q = \dfrac{1}{3y}$